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A245573
Minimal coin changing sequence for denominations 1, 2, 5 and 10 cents.
2
0, 1, 1, 2, 2, 1, 2, 2, 3, 3, 1, 2, 2, 3, 3, 2, 3, 3, 4, 4, 2, 3, 3, 4, 4, 3, 4, 4, 5, 5, 3, 4, 4, 5, 5, 4, 5, 5, 6, 6, 4, 5, 5, 6, 6, 5, 6, 6, 7, 7, 5, 6, 6, 7, 7, 6, 7, 7, 8, 8, 6, 7, 7, 8, 8, 7, 8, 8, 9, 9, 7, 8, 8, 9, 9, 8, 9, 9, 10, 10, 8, 9, 9, 10, 10, 9, 10, 10, 11, 11, 9, 10, 10, 11, 11, 10, 11, 11, 12, 12, 10, 11, 11, 12
OFFSET
0,4
LINKS
Bailor Tow, Coin changing problem, Maths StackExchange
FORMULA
From Colin Barker, Feb 22 2017: (Start)
a(n) = a(n-1) + a(n-10) - a(n-11) for n>10.
G.f.: x*(1 + x^2 - x^4 + x^5 + x^7 - 2*x^9) / ((1 - x)^2*(1 + x)*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)).
(End)
MATHEMATICA
CoefficientList[Series[x (1 + x^2 - x^4 + x^5 + x^7 - 2 x^9)/((1 - x)^2*(1 + x) (1 - x + x^2 - x^3 + x^4) (1 + x + x^2 + x^3 + x^4)), {x, 0, 103}], x] (* Michael De Vlieger, Feb 22 2017 *)
PROG
(PARI) concat(0, Vec(x*(1 + x^2 - x^4 + x^5 + x^7 - 2*x^9) / ((1 - x)^2*(1 + x)*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)) + O(x^100))) \\ Colin Barker, Feb 22 2017
CROSSREFS
Sequence in context: A137419 A057536 A245574 * A236968 A345220 A265744
KEYWORD
nonn,easy
AUTHOR
Marko Riedel, Jul 25 2014
EXTENSIONS
a(0)=0 prepended by Alois P. Heinz, May 26 2015
STATUS
approved